From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 1682 invoked by alias); 3 Jul 2008 11:47:17 -0000 Received: (qmail 1669 invoked by uid 22791); 3 Jul 2008 11:47:17 -0000 X-Spam-Check-By: sourceware.org Received: from mail.network-theory.co.uk (HELO mail.network-theory.co.uk) (66.199.228.187) by sourceware.org (qpsmtpd/0.31) with ESMTP; Thu, 03 Jul 2008 11:47:00 +0000 Date: Thu, 03 Jul 2008 11:47:00 -0000 Message-ID: <87fxqrkx5b.wl%bjg@network-theory.co.uk> From: Brian Gough To: jhu_80@yahoo.com Cc: gsl-discuss@sourceware.org Subject: Re: Library for FT alpha-Stable ch.f. (fwd) In-Reply-To: References: User-Agent: Wanderlust/2.14.0 (Africa) Emacs/22.1 Mule/5.0 (SAKAKI) MIME-Version: 1.0 (generated by SEMI 1.14.6 - "Maruoka") Content-Type: text/plain; charset=US-ASCII X-Message-Mac: e1fda1aa1a54f66b887d074f65bde7cc Mailing-List: contact gsl-discuss-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sourceware.org X-SW-Source: 2008-q3/txt/msg00001.txt.bz2 At Wed, 2 Jul 2008 11:55:32 -0600 (MDT), James Theiler wrote: > I reading thru the source code for the Levy library written for GNU. The statistical model that we are studying is like alpha-stable as only the ch.f. is in closed form. It will be presented this autumn in Melbourne, AU. > > Have you already considered using Fast Fourier transform for the Fourier transform integral? > p(x) dx = (1/(2 pi)) \int dt exp(- it x - |c t|^alpha) > If so, was the Frequency Sampling Technique applied in FFT/IFFT adaptive to the alpha parameter for faster computation? Or was there a bound placed on alpha to imply out Nyquist frequency for your IFFT/FFT? I look forward to your input. Thank you for your time and consideration. The FFT method was too complicated for our needs as a general purpose library so I did not look at it. We only provide cumulative distribution functions when they are available in closed form. -- Brian Gough